Hypothetical
September 25, 2018 4:12 AM   Subscribe

With a very short proof, mathematician Michael Atiyah claims to have solved the Riemann Hypothesis
posted by fearfulsymmetry (30 comments total) 17 users marked this as a favorite
 
The solution to the Reimann hypothesis was one of the solutions required for Mind Candy's first game, a self-supporting ARG called Perplex City. Our own adrienhon was one of the designers of that game.

I'm hoping they update the website to accept this solution, if it's verified.
posted by Merus at 4:29 AM on September 25, 2018 [4 favorites]




This has been greeted by the relevant mathematical community, with some scepticism
posted by talos at 4:38 AM on September 25, 2018 [1 favorite]


John Baez's twitter thread explains some of the skepticism: https://threadreaderapp.com/thread/1043975994246291456.html

Highly recommended -- there's a lot of useful exposition there about the RH, along with his reaction. Baez also links to video of Atiyah's lecture and to a copy of his (Atiyah's) manuscript on the fine structure constant that the RH claims lean heavily upon.

Also, from the Science piece:
Science contacted several of Atiyah’s colleagues. They all expressed concern about his desire to come out of retirement to present proofs based on shaky associations and said it was unlikely that his proof of the Riemann hypothesis would be successful. But none wanted to publicly criticize their mentor or colleague for fear of jeopardizing the relationship.
This is definitely consistent with what I've been seeing in my little circles, but not so much out of fear than out of respect and sadness/concern. :(
posted by Westringia F. at 4:43 AM on September 25, 2018 [13 favorites]




If you are looking for mathematical accuracy in 1970s Antihero's link, stop:
Quick refresher: real numbers are those can be considered as points on a line, whereas imaginary numbers such as -1, which is represented as i, cannot. Thus, for example, 3 + 5 i is a complex number.

Yikes.
posted by King Bee at 5:28 AM on September 25, 2018 [4 favorites]


Well you need a plane to represent them, right?
posted by thelonius at 5:30 AM on September 25, 2018


Well, I guess they said you can't represent i on a line. But you do need a plane for 3 +5i.
posted by thelonius at 5:32 AM on September 25, 2018


John Baez's twitter thread explains some of the skepticism

I'll be the first to admit that I read that as "Joan Baez's twitter thread" and was confused and impressed that a folk singer would tweet to her fans about math.
posted by jonathanhughes at 5:32 AM on September 25, 2018 [27 favorites]


I think they meant square root of -1, not -1 itself.
posted by King Bee at 5:46 AM on September 25, 2018 [4 favorites]


Joan is John's cousin!
posted by Westringia F. at 5:47 AM on September 25, 2018 [37 favorites]


I think they meant square root of -1, not -1 itself.

I didn't even notice that!
posted by thelonius at 5:52 AM on September 25, 2018


If you are looking for mathematical accuracy in 1970s Antihero's link, stop:
... Thus, for example, 3 + 5i is a complex number.

Yikes.


Yikes, indeed. He said "i" when he meant "j".

/EE
posted by ZenMasterThis at 6:17 AM on September 25, 2018 [29 favorites]


I will indeed be very pleased to award Atiyah his Perplex Points upon presentation of a verified solution - no doubt the true motivation behind his work!
posted by adrianhon at 6:21 AM on September 25, 2018 [8 favorites]


"But many experts doubt its validity, especially because Atiyah, 89, has been making mistakes in recent years." =(
posted by rmmcclay at 6:23 AM on September 25, 2018 [1 favorite]


"But many experts doubt its validity, especially because Atiyah, 89, has been making mistakes in recent years." =(

While there is a certain tragic grandeur in the concept of a sort of mathematical King Lear, driven onto the heath with his chalkboard and his Fool, it is mostly sad to contemplate.
posted by thelonius at 6:40 AM on September 25, 2018 [5 favorites]


This is quite balanced a take on Atiyah's claimed proof. Without much drama or bitterness.
posted by runcifex at 7:06 AM on September 25, 2018 [9 favorites]


This isn’t the first time Michael Atiyah has claimed to crack a big math problem and never followed up the claims with publication, however.

Also not the first time someone's claim to have proven the Riemann hypothesis hasn't quite held up...
posted by Naberius at 7:53 AM on September 25, 2018


This is tied into a claim about the fine structure constant, as is mentioned in many of the links already. Sean Carroll weighs in on that side of things but not on the Riemann side.
posted by edd at 8:13 AM on September 25, 2018 [4 favorites]


> Also not the first time someone ...

Please let us not lump Atiyah in with cranks and plagiarists. Atiyah may be mistaken (and there are good arguments that he is), but he is not, by any stretch, a crank. There is absolutely no comparison between this & the scammer from Naberius' link.
posted by Westringia F. at 8:36 AM on September 25, 2018 [11 favorites]


Weird how there's an indepth maths article on Vice magazine's website. Will we now see serious journals doing exploitative pieces on Russian krokodil users to balance it out?!?
posted by JonB at 8:42 AM on September 25, 2018 [4 favorites]


Weird how there's an indepth maths article on Vice magazine's website. Will we now see serious journals doing exploitative pieces on Russian krokodil users to balance it out?!?

Publishing isn't a zero-sum ga...oh, was that the joke? I need more coffee.
posted by Revvy at 9:10 AM on September 25, 2018 [1 favorite]


Also not the first time someone's claim to have proven the Riemann hypothesis hasn't quite held up ...

Did not G. H. Hardy write in his Apology that, before he set off on any oceanic voyage, he would mail a postcard to a colleague, with a claim to have solved the Riemann Hypothesis? Thus he would dare fate to immortalise him, should it choose to mortalise him.

For similar reasons: whenever attending an airport I always purchase a paperback novella, note therein a criticism of its margins as spatially inadequate for a full explication of my proof of the Goldbach Conjecture, and gift said literary work to any passing customs official.
posted by the quidnunc kid at 9:14 AM on September 25, 2018 [20 favorites]


Please let us not lump Atiyah in with cranks and plagiarists. Atiyah may be mistaken (and there are good arguments that he is), but he is not, by any stretch, a crank.

I think some people are beating around the bush in an effort to be respectful and making Atiyah look worse than he should. He's a very respected figure - people are skeptical of this claim because he's almost 90 years old and the track record of his big claims in the last few years is not great.
posted by atoxyl at 9:34 AM on September 25, 2018 [2 favorites]


Please let us not lump Atiyah in with cranks and plagiarists. Atiyah may be mistaken (and there are good arguments that he is), but he is not, by any stretch, a crank. There is absolutely no comparison between this & the scammer from Naberius' link.

I respect your viewpoint, but I think you've imputed a moral dimension to crankdom that's inappropriate. Cranks are people who are unable to produce good proofs and who cannot be convinced of their falsity. Cranks are not bad people, they are unfortunates who have lost the intellectual and social capacity to participate in mathematics. Sir Atiyah should be put among their number because he has in old age become one of them.
posted by TypographicalError at 9:36 AM on September 25, 2018 [1 favorite]


I have a more thorough and intricate proof of this theorem.

Unfortunately, my bus is here.
posted by delfin at 9:43 AM on September 25, 2018 [13 favorites]


Delfin, be careful. That bus will explode if it ever drops below the answer to the hypothesis.
posted by GoblinHoney at 10:24 AM on September 25, 2018


About 80% of the first link is over my head, but here's what I gather from it (just commenting on the alleged RH proof, not on the link to the fine structure constant):

1. Atiyah talks about the "Todd function," or T(s), and describes certain properties of it, but critically, does not define T(s) itself. Says T(s) is defined in a paper submitted to Proceedings of the Royal Society of London A.
2. Then goes on to show that if T(s) exists with the described properties, (and the axiom of choice is true) a proof of RH follows.

As far as I can tell, everything which is necessary to evaluate the validity of step 2 is in that first paper. Meaning, if there were a problem with step 2, some other mathematician would have noticed pretty quickly (I assume, I could be wrong). Which means the validity of the proof hangs on the existence of a function T(s) which has the described properties. And that can't be evaluated without seeing Atiyah's definition of T(s) in the paper submitted to Proceedings A, which has not been published...

... or hadn't. The piece from John D. Cook which runcifex linked above has an update: "The longer paper has been leaked, presumably without permission from Atiyah or the Royal Society, and it doesn’t seem to hold up."
posted by DevilsAdvocate at 1:57 PM on September 25, 2018


His proof explained.
posted by Wet Spot at 3:12 PM on September 25, 2018


King Bee - on my device, it properly shows as sqrt(-1), so chances are it's either a font / rendering issue in some browsers, or they fixed it now!
posted by Greasy Eyed Gristle Man at 7:43 AM on September 26, 2018


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